A Researcher Wants to Examine How the Remaining Balance on $100,000

question 103

Multiple Choice

A researcher wants to examine how the remaining balance on $100,000 loans taken 10 to 20 years ago depends on whether the loan was a prime or subprime loan. He collected a sample of 25 prime loans and 25 subprime loans and recorded the data in the following variables: Balance = the remaining amount of loan to be paid off (in $) ,
Time = the time elapsed from taking the loan,
Prime = a dummy variable assuming 1 for prime loans, and 0 for subprime loans.
The regression results obtained for the models:
Model A: Balance = β₀ + β₁Prime + ε
Model B: Balance = β₀ + β₁Time + β₂Prime + β₃Time × Prime + ε
Model C: Balance = β₀ + β₁Prime + β₂Time × Prime + ε,
Are summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients.
Suppose that at a 10% significance level, you do not reject the null hypothesis, H₀: β₁ = 0, when testing the individual significance of Time in Model B. Would you delete Time from Model B?

• A) Yes, removing Time from Model B results in Model C which has a higher adjusted R².
• B) No, removing Time from Model B results in Model C which has a with lower R².
• C) No, Model B has the highest R², so it should be used for making predictions.
• D) Yes, Time should be deleted because we could not prove its significance even for α = 0.10.

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Definitions:

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